In the earlier devices of this kind, the winding magazine is provided with its own drive, which moves the magazine disks, step by step, for instance each by 90.degree. in such a manner that the roll cores lying in the roll-core receiving portions are successively brought to the winding device and received by it, when a foil roll is finished and it is necessary to prepare the winding operation for a new foil roll. It is self-understood that the foil web then must be separated by a sectioning device, that the trailing end of the foil web resulted from the sectioning has to exit the device with the foil roll and that the leading edge of the remaining foil web has to be wound around the new roll core. For this purpose, the winding arms have to be properly moved. All this is cumbersome and requires correspondingly synchronizable drives and controls. Generally, the roll cores are introduced manually into the receiving portions of the magazine disks.